The GATE Grind

GATE 2020 CH – Question 15

Fluid Mechanics and Mechanical Operations · Settling, centrifuges, cyclones, thickening, filtration, agitation and mixing · 1 mark · Multiple choice

For constant-pressure filtration with incompressible cake, a plot of t/V versus filtrate volume V is linear with intercept $10^4$ s/m³. Filter area is 0.05 m², viscosity is $10^{-3}$ Pa s and pressure drop is 200 kPa. Find filter-medium resistance in m⁻¹.

  1. $10^9$
  2. $10^{10}$
  3. $10^{11}$
  4. $10^{12}$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) $10^{11}$

Explanation

The integrated constant-pressure filtration equation is $t/V=\mu\alpha cV/(2A^2\Delta P)+\mu R_m/(A\Delta P)$. Its intercept is $b=\mu R_m/(A\Delta P)$. Therefore $R_m=bA\Delta P/\mu=10^4(0.05)(200000)/10^{-3}=10^{11}$ m⁻¹, C. The cake coefficient determines the slope, not this intercept.

More Settling, centrifuges, cyclones, thickening, filtration, agitation and mixing questions

All Settling, centrifuges, cyclones, thickening, filtration, agitation and mixing questions →